A video signal may be represented in various spaces interlinked by a transfer function. Thus, the representation space for the colour levels consists of a set of integers, varying for example between 0 and 255. The visualization space is, for its part, the space in which the optical signal is generated and perceived.
In most video image display devices, the representation space for the colour levels and the visualization space are related by a nonlinear law called the electro-optical transfer function or more commonly the gamma law. The luminous intensity reproduced on the screen is therefore a nonlinear function of the colour level at the input of the display device.
The transfer function relating the two representation spaces is characteristic of the type of display device. In the case of cathode ray tubes, the gamma law of the tube has the following form:
      n    out    =            N      out        ·                  (                              n                          i              ⁢                                                          ⁢              n                                            N                          i              ⁢                                                          ⁢              n                                      )            γ                      nin is the input level,        nout is the output level,        Nin is the maximum level characterizing nin,        Nout is the maximum level characterizing nout,        γ is the coefficient characterizing the transfer function.        
According to the state of the art, it is known, in order to estimate the gamma law of a display device, to display on the latter a series of uniform images whose level varies from 0 to 255. We then measure the light level L(n) emitted by the screen for each input level n, then we normalize this curve by the maximum of these input levels: γ=255*L(n)/L(255).
FIG. 1 and FIG. 2 illustrate a method of processing according to the state of the art of a video signal pre-corrected (FIG. 1) or not (FIG. 2) by an inverse gamma law, aimed at reducing the visual defects due to the display device.
The transfer function (also called the posterior law subsequently in the document), described previously and referenced 15 in FIG. 1, has the feature of attenuating the dark pixels. It is known to pre-correct the initial video signal arising from the camera by an inverse gamma law 11 (also called the anterior law subsequently in the document) so as to compensate for this attenuation before transmitting this signal corrected to the display device. This processing which is generally performed at the level of the camera is not mandatory. The value of gamma used to pre-correct the initial video signal is known and specified in various documents in particular the Recommendations of the ITU for television (e.g. ITU-R BT.709-5, Basic Parameters Values for HDTV, ITU-R BT.470-6, Conventional Television System).
In addition, before displaying the video signal transmitted on the screen, it may be necessary to apply a video processing 13 to the pre-corrected or not pre-corrected video signals so as for example to improve the quality of the signal which will be displayed. The video processing may, for example, be a re-interpolation of video images aimed at correcting distortions in the images. The distortions are due to the display device.
When such a video processing is applied, it is necessary to work in a space which is linear with respect to the visualization space. Specifically, in the converse case we would see the appearance on the displayed image of processing dependent defects. For example, in the case of a re-interpolation the brightness of a point of the image may vary depending on whether it is re-interpolated on one or on n pixels. Specifically, in this case, the visual sum of the intensities of the n pixels is not the same as that of the pixel alone if the processing space is not a linear space with respect to the visualization space.
For this purpose, as illustrated in FIG. 1, it is known to invert on either side of the processing block 13, the anterior law 11 if the initial signal has been pre-corrected and to invert the posterior law 15, respectively in the blocks 12 and 14. The display device modifies according to the gamma law characteristic of the display device the video signal thus corrected.
However, as described previously, a video signal may be generated and produced by the camera without having previously been pre-corrected by an inverse gamma law 11. In this case, as illustrated in FIG. 2, it is known to apply the video processing directly to the initial video signal 21. The signal thus obtained is corrected by an inverse gamma law 22, so as to compensate for the attenuation of the dark points introduced by the transfer function of the tube. The display device 23 modifies the video signal thus corrected according to the gamma law characteristic of the display device.
The method according to the state of the art, though it makes it possible to correct certain defects (for example attenuation of the dark points), does not take account of certain characteristics of certain display devices which depend on the direction of visualization (e.g. inter-pixel overlap, shape of the spot).
Thus, in the case of the application of video processing which successively applies to the horizontal (X) and vertical components of the image (Y), the application of a global gamma law may cause visual defects. The term global gamma law signifies a law which applies in the same manner whether we process the vertical or horizontal components of the video signal. Defects of local attenuation of the red, green and blue signals, generating colour defects are, for example, visible in the case where we apply a processing of re-interpolation of a colour image.
It is therefore desirable in order to process the video signal to take account of the direction (horizontal or vertical) of processing.